Resonant tori and instabilities in Hamiltonian systems
نویسندگان
چکیده
The existence of lower-dimensional resonant bifurcating tori of parabolic, hyperbolic and elliptic normal stability types is proved to be generic and persistent in a class of n degrees of freedom (DOF) integrable Hamiltonian systems with n 3. Parabolic resonance (PR) (respectively, hyperbolic or elliptic resonance) is created when a small Hamiltonian perturbation is added to an integrable Hamiltonian system possessing a resonant torus of the corresponding normal stability. It is numerically demonstrated that PRs cause intricate behaviour and large instabilities. The role of lower-dimensional bifurcating resonant tori in creation of instability mechanisms is illustrated using phenomenological models of near integrable Hamiltonian systems with 3, 4 and 5 DOF. Criticaln values for which the system first persistently possesses mechanisms for large instabilities of a certain type are found. Initial numerical studies of the rate and time of development of the most significant instabilities are presented. Mathematics Subject Classification: 37J35, 70H14, 37J20, 37J40, 70H08
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تاریخ انتشار 2002